Brownian motion moves beyond Einstein’s equations

Scientists have verified there are nuances to particle movement and energy at …

There are nuances to particle movement and energy at tiny scales that one of Einstein's equations did not capture, according to a paper published in Science this week. Researchers were able to measure the instantaneous velocity of a tiny glass bead undergoing Brownian motion, or making tiny random movements, and found that the particle was not always governed by the forces that Einstein predicted. Knowing how Brownian motion works at these short intervals may allow researchers to study these tiny particle systems for quantum effects.

Barring extreme cold, particles are usually not sitting still, but exhibit a kind of hyperactivity, always moving tiny distances in random directions. This is called Brownian motion, and it can be described by equations that relate the distance moved to the time involved, the drag of the medium, and the temperature of the particle's environment.

Einstein himself developed the equations we typically use to predict Brownian motion. However, scientists had begun to suspect that there was more involved with Brownian motion than these equations indicated.

They thought it might be possible that the diffusive effects in these formulae, which depend on drag (among other things) will only become significant once some time has elapsed. In short intervals—around a few microseconds—a particle's movement could be ballistic, dominated by its own inertia, before drag gets a chance to kick in.

To detect any period of ballistic movement, researchers had to study a particle's movements where drag was low in the first place. Drag is higher in water, so they chose to use a gaseous environment. They also decided to vary the air pressure, thereby varying the drag coefficient. If the particle movement was the same for different drag coefficients, they could infer that they were seeing the particle move too quickly for drag effects.

The testing environment used pressures from 1 to .027 atmospheres. Researchers suspended a glass bead with two lasers that made a harmonic potential for the bead to sit in. They then measured the bead's Brownian movements at various air pressures by tracking the deflection of one of the beams, and used the movement times to calculate the bead's instantaneous velocity.

The suspicions were correct: the particle's movement over spans of a few microseconds depended on its mass and temperature, but did not depend on the air pressure and drag coefficients. The particles moved as if they were in a complete vacuum.

Another longstanding question has been answered here too. Physicists have been uncertain about whether Brownian particles may be governed by the equipartition theorem, a thermodynamic rule saying a particle's mean movement is directly proportional to its temperature, and only its temperature, when it is in thermal equilibrium with its environment.

At least for particles moving for short times in a gas, the equipartition theorem holds—the only environmental factor that affects it is the temperature. However, researchers couldn't test the equation with more viscous mediums like liquid, because drag engages in nanoseconds instead of microseconds, and the ballistic motion ends too quickly to be detected.

Still, knowing this new quirk of Brownian motion in lighter mediums could help scientists develop better feedback mechanisms that act in the opposite direction of the particle's velocity to keep it still. This would eliminate the influence of temperature as well, and could in theory counter all Brownian motion.

If the particle is not able to squiggle around as much, scientists could get better measurements of its quantum characteristics. Still, they are open to the possibility that there may be more motion subtleties to Brownian motion than the ballistic motion they appear to have come to grips with.